| Algorithm 1 SSM (S4) | Algorithm 2 SSM + Selection (S6) |
| Input: x : (B,L,D) | Input: x : (B,L,D) |
| Output: y:(B,L,D) | Output: y: (B,L,D) |
| 1:A:(D,N)←Parameter | 1:A:(D,N)←Parameter |
| Represents structured N × N matrix | >Represents structured N × N matrix |
| 2:B:(D,N)←Parameter | 2: B:(B,L,N)← SB(𝑥) |
| 3: C:(D,N)←Parameter | 3: C:(B,L,N)←sc(x) |
| 4:△:(D)←T△(Parameter) | 4: △:(B,L,D)←T△(Parameter+s△(x)) |
| 5: A,B:(D,N)←discretize(△,A,B) | 5: A,B:(B,L,D,N)←discretize(△,A,B) |
| 6: y←SSM(A,B,C)(x) | 6: y←SSM(A,B,C)(x) |
| > Time-invariant: recurrence or convolution 7: return y | Time-varying: recurrence (scan) only 7: return y |
"
},
{
"category_id": 1,
"poly": [
299,
746,
1400,
746,
1400,
837,
299,
837
],
"score": 0.955
},
{
"category_id": 1,
"poly": [
300,
1291,
1403,
1291,
1403,
1352,
300,
1352
],
"score": 0.935
},
{
"category_id": 0,
"poly": [
298,
1869,
863,
1869,
863,
1900,
298,
1900
],
"score": 0.912
},
{
"category_id": 1,
"poly": [
297,
848,
1404,
848,
1404,
1009,
297,
1009
],
"score": 0.904
},
{
"category_id": 0,
"poly": [
302,
1513,
789,
1513,
789,
1544,
302,
1544
],
"score": 0.9
},
{
"category_id": 2,
"poly": [
300,
76,
844,
76,
844,
104,
300,
104
],
"score": 0.887
},
{
"category_id": 2,
"poly": [
841,
2088,
858,
2088,
858,
2112,
841,
2112
],
"score": 0.719
},
{
"category_id": 13,
"poly": [
475,
1974,
527,
1974,
527,
2007,
475,
2007
],
"score": 0.92,
"latex": "s ( x )"
},
{
"category_id": 13,
"poly": [
755,
848,
890,
848,
890,
882,
755,
882
],
"score": 0.91,
"latex": "O ( B L D N )"
},
{
"category_id": 13,
"poly": [
749,
1750,
840,
1750,
840,
1781,
749,
1781
],
"score": 0.9,
"latex": "( 3 E D ^ { 2 } )"
},
{
"category_id": 13,
"poly": [
672,
1781,
739,
1781,
739,
1808,
672,
1808
],
"score": 0.9,
"latex": "E = 2"
},
{
"category_id": 13,
"poly": [
340,
525,
576,
525,
576,
557,
340,
557
],
"score": 0.89,
"latex": "y \\mathsf { S S M } ( \\overline { { A } } , \\overline { { B } } , C ) ( x )"
},
{
"category_id": 13,
"poly": [
337,
1808,
403,
1808,
403,
1838,
337,
1838
],
"score": 0.89,
"latex": "1 2 D ^ { 2 }"
},
{
"category_id": 13,
"poly": [
1243,
384,
1315,
384,
1315,
409,
1243,
409
],
"score": 0.88,
"latex": "N \\times N"
},
{
"category_id": 13,
"poly": [
728,
1218,
870,
1218,
870,
1250,
728,
1250
],
"score": 0.88,
"latex": "( \\Delta , A , B , C )"
},
{
"category_id": 13,
"poly": [
799,
1184,
878,
1184,
878,
1219,
799,
1219
],
"score": 0.87,
"latex": "( \\overline { { A } } , \\overline { { B } } )"
},
{
"category_id": 13,
"poly": [
375,
879,
560,
879,
560,
913,
375,
913
],
"score": 0.86,
"latex": "O ( B L D \\log ( L ) )"
},
{
"category_id": 13,
"poly": [
698,
383,
770,
383,
770,
409,
698,
409
],
"score": 0.85,
"latex": "N \\times N"
},
{
"category_id": 13,
"poly": [
341,
410,
461,
410,
461,
438,
341,
438
],
"score": 0.85,
"latex": "B : ( \\mathbb { D } , \\mathbb { N } ) \\gets"
},
{
"category_id": 13,
"poly": [
884,
525,
1120,
525,
1120,
557,
884,
557
],
"score": 0.85,
"latex": "y \\mathsf { S S M } ( \\overline { { A } } , \\overline { { B } } , C ) ( x )"
},
{
"category_id": 13,
"poly": [
340,
465,
469,
465,
469,
493,
340,
493
],
"score": 0.83,
"latex": "\\Delta \\colon ( \\mathsf { D } ) \\gets \\tau _ { \\Delta }"
},
{
"category_id": 13,
"poly": [
341,
438,
461,
438,
461,
465,
341,
465
],
"score": 0.83,
"latex": "C : ( \\mathtt { D } , \\mathtt { N } ) \\gets"
},
{
"category_id": 13,
"poly": [
886,
410,
1093,
410,
1093,
438,
886,
438
],
"score": 0.82,
"latex": "B : ( { \\mathbb { B } } , { \\mathbb { L } } , { \\mathbb { N } } ) \\gets s _ { B } \\bar { ( } x )"
},
{
"category_id": 13,
"poly": [
341,
357,
461,
357,
461,
386,
341,
386
],
"score": 0.81,
"latex": "\\pmb { A } : ( \\mathbb { D } , \\mathbb { N } ) \\gets"
},
{
"category_id": 13,
"poly": [
1374,
1722,
1398,
1722,
1398,
1748,
1374,
1748
],
"score": 0.79,
"latex": "E"
},
{
"category_id": 13,
"poly": [
693,
911,
721,
911,
721,
937,
693,
937
],
"score": 0.78,
"latex": "N"
},
{
"category_id": 13,
"poly": [
1060,
644,
1087,
644,
1087,
670,
1060,
670
],
"score": 0.78,
"latex": "\\Delta"
},
{
"category_id": 13,
"poly": [
341,
493,
491,
493,
491,
524,
341,
524
],
"score": 0.77,
"latex": "\\overline { { A } } , \\overline { { B } } : \\left( \\mathbb { D } , \\mathbb { N } \\right) \\gets"
},
{
"category_id": 13,
"poly": [
887,
438,
1093,
438,
1093,
465,
887,
465
],
"score": 0.76,
"latex": "C : ( \\mathbb { B } , \\mathbb { L } , \\mathbb { N } ) \\gets s _ { C } ( x )"
},
{
"category_id": 13,
"poly": [
957,
1722,
984,
1722,
984,
1748,
957,
1748
],
"score": 0.75,
"latex": "D"
},
{
"category_id": 13,
"poly": [
1380,
979,
1398,
979,
1398,
1005,
1380,
1005
],
"score": 0.74,
"latex": "h"
},
{
"category_id": 13,
"poly": [
885,
357,
1006,
357,
1006,
386,
885,
386
],
"score": 0.72,
"latex": "\\scriptstyle A : ( \\mathtt { D } , \\mathtt { N } ) \\gets"
},
{
"category_id": 13,
"poly": [
1381,
1022,
1402,
1022,
1402,
1049,
1381,
1049
],
"score": 0.71,
"latex": "h"
},
{
"category_id": 13,
"poly": [
946,
331,
1047,
331,
1047,
357,
946,
357
],
"score": 0.69,
"latex": "y : \\left( \\mathtt { B } , \\mathtt { L } , \\mathtt { D } \\right)"
},
{
"category_id": 13,
"poly": [
384,
301,
487,
301,
487,
330,
384,
330
],
"score": 0.69,
"latex": "x : \\left( \\mathtt { B } , \\mathtt { L } , \\mathtt { D } \\right)"
},
{
"category_id": 13,
"poly": [
885,
493,
1076,
493,
1076,
524,
885,
524
],
"score": 0.66,
"latex": "\\overline { { A } } , \\overline { { B } } : ( \\mathrm { B , L , D , N } ) "
},
{
"category_id": 13,
"poly": [
989,
1945,
1015,
1945,
1015,
1971,
989,
1971
],
"score": 0.63,
"latex": "\\pmb { A }"
},
{
"category_id": 13,
"poly": [
929,
301,
1031,
301,
1031,
330,
929,
330
],
"score": 0.61,
"latex": "\\scriptstyle x : \\left( { \\mathtt { B } } , { \\mathtt { L } } , { \\mathtt { D } } \\right)"
},
{
"category_id": 13,
"poly": [
413,
586,
431,
586,
431,
610,
413,
610
],
"score": 0.51,
"latex": "_ y"
},
{
"category_id": 13,
"poly": [
887,
465,
1274,
465,
1274,
492,
887,
492
],
"score": 0.45,
"latex": "\\Delta \\smash { : ( \\mathbb { B } , \\mathbb { L } , \\mathbb { D } ) } \\{ \\ - \\tau _ { \\Delta } \\bigl ( \\mathsf { P a r a m e t e r } + \\boldsymbol { s } _ { \\Delta } ( x ) \\bigr )"
},
{
"category_id": 13,
"poly": [
402,
331,
504,
331,
504,
357,
402,
357
],
"score": 0.4,
"latex": "y : \\left( \\mathtt { B } , \\mathtt { L } , \\mathtt { D } \\right)"
},
{
"category_id": 13,
"poly": [
402,
332,
420,
332,
420,
356,
402,
356
],
"score": 0.38,
"latex": "_ y"
},
{
"category_id": 13,
"poly": [
886,
466,
1056,
466,
1056,
492,
886,
492
],
"score": 0.36,
"latex": "\\Delta : ( \\mathtt { B } , \\mathtt { L } , \\mathtt { D } ) \\tau _ { \\Delta }"
},
{
"category_id": 13,
"poly": [
1004,
387,
1023,
387,
1023,
408,
1004,
408
],
"score": 0.34,
"latex": "\\triangleright"
},
{
"category_id": 13,
"poly": [
339,
493,
692,
493,
692,
524,
339,
524
],
"score": 0.34,
"latex": "\\overline { { A } } , \\overline { { B } } : ( \\mathbb { D } , \\mathbb { N } ) \\longleftarrow \\mathsf { d i s c r e t i z e } ( \\Delta , A , B )"
},
{
"category_id": 13,
"poly": [
592,
494,
691,
494,
691,
524,
592,
524
],
"score": 0.33,
"latex": "^ { ( \\Delta , A , B ) }"
},
{
"category_id": 13,
"poly": [
459,
387,
479,
387,
479,
408,
459,
408
],
"score": 0.33,
"latex": "\\triangleright"
},
{
"category_id": 13,
"poly": [
1173,
465,
1260,
465,
1260,
493,
1173,
493
],
"score": 0.29,
"latex": "+ s _ { \\Delta } ( x )"
},
{
"category_id": 13,
"poly": [
1175,
494,
1277,
494,
1277,
524,
1175,
524
],
"score": 0.25,
"latex": "( \\Delta , A , B )"
},
{
"category_id": 15,
"poly": [
293.0,
1865.0,
867.0,
1865.0,
867.0,
1905.0,
293.0,
1905.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
296.0,
1512.0,
795.0,
1512.0,
795.0,
1547.0,
296.0,
1547.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
297.0,
73.0,
848.0,
73.0,
848.0,
108.0,
297.0,
108.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
839.0,
2085.0,
861.0,
2085.0,
861.0,
2120.0,
839.0,
2120.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
297.0,
1558.0,
1405.0,
1558.0,
1405.0,
1591.0,
297.0,
1591.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
295.0,
1588.0,
1404.0,
1588.0,
1404.0,
1621.0,
295.0,
1621.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
294.0,
1617.0,
1405.0,
1617.0,
1405.0,
1653.0,
294.0,
1653.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
293.0,
1640.0,
1405.0,
1640.0,
1405.0,
1686.0,
293.0,
1686.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
295.0,
1677.0,
1123.0,
1677.0,
1123.0,
1714.0,
295.0,
1714.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
294.0,
1719.0,
956.0,
1719.0,
956.0,
1755.0,
294.0,
1755.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
985.0,
1719.0,
1373.0,
1719.0,
1373.0,
1755.0,
985.0,
1755.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
1399.0,
1719.0,
1409.0,
1719.0,
1409.0,
1755.0,
1399.0,
1755.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
294.0,
1749.0,
748.0,
1749.0,
748.0,
1785.0,
294.0,
1785.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
841.0,
1749.0,
1408.0,
1749.0,
1408.0,
1785.0,
841.0,
1785.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
295.0,
1782.0,
671.0,
1782.0,
671.0,
1814.0,
295.0,
1814.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
740.0,
1782.0,
1405.0,
1782.0,
1405.0,
1814.0,
740.0,
1814.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
293.0,
1807.0,
336.0,
1807.0,
336.0,
1845.0,
293.0,
1845.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
404.0,
1807.0,
1379.0,
1807.0,
1379.0,
1845.0,
404.0,
1845.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
295.0,
1912.0,
1407.0,
1912.0,
1407.0,
1950.0,
295.0,
1950.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
294.0,
1942.0,
988.0,
1942.0,
988.0,
1980.0,
294.0,
1980.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
1016.0,
1942.0,
1407.0,
1942.0,
1407.0,
1980.0,
1016.0,
1980.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
296.0,
1972.0,
474.0,
1972.0,
474.0,
2006.0,
296.0,
2006.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
528.0,
1972.0,
1404.0,
1972.0,
1404.0,
2006.0,
528.0,
2006.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
295.0,
2002.0,
1404.0,
2002.0,
1404.0,
2036.0,
295.0,
2036.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
294.0,
1364.0,
1409.0,
1364.0,
1409.0,
1400.0,
294.0,
1400.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
293.0,
1393.0,
1406.0,
1393.0,
1406.0,
1430.0,
293.0,
1430.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
294.0,
1426.0,
1405.0,
1426.0,
1405.0,
1459.0,
294.0,
1459.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
294.0,
1454.0,
1263.0,
1454.0,
1263.0,
1489.0,
294.0,
1489.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
296.0,
1021.0,
1380.0,
1021.0,
1380.0,
1054.0,
296.0,
1054.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
296.0,
1051.0,
1405.0,
1051.0,
1405.0,
1084.0,
296.0,
1084.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
294.0,
1080.0,
1405.0,
1080.0,
1405.0,
1113.0,
294.0,
1113.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
294.0,
1108.0,
1406.0,
1108.0,
1406.0,
1144.0,
294.0,
1144.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
293.0,
1139.0,
1242.0,
1139.0,
1242.0,
1174.0,
293.0,
1174.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
295.0,
1185.0,
798.0,
1185.0,
798.0,
1222.0,
295.0,
1222.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
879.0,
1185.0,
1405.0,
1185.0,
1405.0,
1222.0,
879.0,
1222.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
295.0,
1217.0,
727.0,
1217.0,
727.0,
1251.0,
295.0,
1251.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
871.0,
1217.0,
1404.0,
1217.0,
1404.0,
1251.0,
871.0,
1251.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
294.0,
1245.0,
1409.0,
1245.0,
1409.0,
1283.0,
294.0,
1283.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
297.0,
642.0,
1059.0,
642.0,
1059.0,
676.0,
297.0,
676.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
1088.0,
642.0,
1402.0,
642.0,
1402.0,
676.0,
1088.0,
676.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
296.0,
669.0,
1402.0,
669.0,
1402.0,
707.0,
296.0,
707.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
296.0,
701.0,
1354.0,
701.0,
1354.0,
737.0,
296.0,
737.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
292.0,
744.0,
1406.0,
744.0,
1406.0,
782.0,
292.0,
782.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
295.0,
777.0,
1404.0,
777.0,
1404.0,
811.0,
295.0,
811.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
297.0,
806.0,
1324.0,
806.0,
1324.0,
839.0,
297.0,
839.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
298.0,
1290.0,
1403.0,
1290.0,
1403.0,
1321.0,
298.0,
1321.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
294.0,
1316.0,
1408.0,
1316.0,
1408.0,
1355.0,
294.0,
1355.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
292.0,
846.0,
754.0,
846.0,
754.0,
886.0,
292.0,
886.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
891.0,
846.0,
1404.0,
846.0,
1404.0,
886.0,
891.0,
886.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
317.0,
878.0,
374.0,
878.0,
374.0,
916.0,
317.0,
916.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
561.0,
878.0,
1405.0,
878.0,
1405.0,
916.0,
561.0,
916.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
319.0,
909.0,
692.0,
909.0,
692.0,
943.0,
319.0,
943.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
722.0,
909.0,
1280.0,
909.0,
1280.0,
943.0,
722.0,
943.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
295.0,
943.0,
1404.0,
943.0,
1404.0,
983.0,
295.0,
983.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
317.0,
976.0,
1379.0,
976.0,
1379.0,
1014.0,
317.0,
1014.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
1399.0,
976.0,
1409.0,
976.0,
1409.0,
1014.0,
1399.0,
1014.0
],
"score": 1.0,
"text": ""
}
],
"page_info": {
"page_no": 4,
"width": 1700,
"height": 2200
}
},
{
"layout_dets": [
{
"category_id": 1,
"poly": [
298,
941,
1405,
941,
1405,
1093,
298,
1093
],
"score": 0.976
},
{
"category_id": 1,
"poly": [
297,
1312,
1404,
1312,
1404,
1493,
297,
1493
],
"score": 0.976
},
{
"category_id": 3,
"poly": [
435,
223,
1264,
223,
1264,
551,
435,
551
],
"score": 0.974
},
{
"category_id": 1,
"poly": [
297,
1149,
1405,
1149,
1405,
1300,
297,
1300
],
"score": 0.974
},
{
"category_id": 1,
"poly": [
299,
1504,
1404,
1504,
1404,
1634,
299,
1634
],
"score": 0.973
},
{
"category_id": 1,
"poly": [
299,
1784,
1403,
1784,
1403,
1875,
299,
1875
],
"score": 0.971
},
{
"category_id": 1,
"poly": [
299,
1943,
1403,
1943,
1403,
2034,
299,
2034
],
"score": 0.97
},
{
"category_id": 1,
"poly": [
298,
726,
1404,
726,
1404,
848,
298,
848
],
"score": 0.968
},
{
"category_id": 4,
"poly": [
297,
576,
1405,
576,
1405,
716,
297,
716
],
"score": 0.959
},
{
"category_id": 1,
"poly": [
297,
1643,
1401,
1643,
1401,
1705,
297,
1705
],
"score": 0.941
},
{
"category_id": 1,
"poly": [
294,
856,
1403,
856,
1403,
921,
294,
921
],
"score": 0.933
},
{
"category_id": 1,
"poly": [
296,
1105,
989,
1105,
989,
1136,
296,
1136
],
"score": 0.925
},
{
"category_id": 0,
"poly": [
299,
1898,
591,
1898,
591,
1930,
299,
1930
],
"score": 0.912
},
{
"category_id": 0,
"poly": [
302,
1733,
706,
1733,
706,
1768,
302,
1768
],
"score": 0.89
},
{
"category_id": 2,
"poly": [
299,
76,
845,
76,
845,
104,
299,
104
],
"score": 0.883
},
{
"category_id": 2,
"poly": [
840,
2089,
858,
2089,
858,
2112,
840,
2112
],
"score": 0.777
},
{
"category_id": 13,
"poly": [
669,
1535,
833,
1535,
833,
1572,
669,
1572
],
"score": 0.93,
"latex": "\\overline { { A } } = \\exp ( \\Delta A )"
},
{
"category_id": 13,
"poly": [
1114,
888,
1398,
888,
1398,
921,
1114,
921
],
"score": 0.93,
"latex": "h _ { k } = ( 1 - g _ { k } ) h _ { k - 1 } + g _ { k } x _ { k }"
},
{
"category_id": 13,
"poly": [
545,
1569,
624,
1569,
624,
1606,
545,
1606
],
"score": 0.9,
"latex": "( \\overline { { A } } , \\overline { { B } } )"
},
{
"category_id": 13,
"poly": [
892,
1270,
969,
1270,
969,
1301,
892,
1301
],
"score": 0.9,
"latex": "g _ { k } \\to 0"
},
{
"category_id": 13,
"poly": [
895,
948,
971,
948,
971,
974,
895,
974
],
"score": 0.9,
"latex": "s \\Delta , \\tau _ { \\Delta }"
},
{
"category_id": 13,
"poly": [
988,
859,
1048,
859,
1048,
888,
988,
888
],
"score": 0.87,
"latex": "\\tau _ { \\Delta } ="
},
{
"category_id": 13,
"poly": [
578,
977,
611,
977,
611,
1003,
578,
1003
],
"score": 0.86,
"latex": "x _ { k }"
},
{
"category_id": 13,
"poly": [
1364,
1243,
1396,
1243,
1396,
1270,
1364,
1270
],
"score": 0.85,
"latex": "x _ { k }"
},
{
"category_id": 13,
"poly": [
726,
1032,
1058,
1032,
1058,
1066,
726,
1066
],
"score": 0.85,
"latex": "s \\bar { \\Delta ( x ) } = \\mathsf { L i n e a r } _ { D } ( \\mathsf { L i n e a r } _ { 1 } ( x ) )"
},
{
"category_id": 13,
"poly": [
739,
889,
952,
889,
952,
921,
739,
921
],
"score": 0.82,
"latex": "g _ { k } { = } \\sigma ( { \\mathsf { L i n e a r } } ( x _ { k } ) )"
},
{
"category_id": 13,
"poly": [
393,
818,
419,
818,
419,
844,
393,
844
],
"score": 0.8,
"latex": "\\Delta"
},
{
"category_id": 13,
"poly": [
600,
1539,
626,
1539,
626,
1566,
600,
1566
],
"score": 0.8,
"latex": "\\Delta"
},
{
"category_id": 13,
"poly": [
700,
1604,
726,
1604,
726,
1630,
700,
1630
],
"score": 0.79,
"latex": "\\Delta"
},
{
"category_id": 13,
"poly": [
298,
1004,
324,
1004,
324,
1030,
298,
1030
],
"score": 0.78,
"latex": "D"
},
{
"category_id": 13,
"poly": [
1263,
1539,
1290,
1539,
1290,
1567,
1263,
1567
],
"score": 0.77,
"latex": "\\Delta"
},
{
"category_id": 13,
"poly": [
517,
856,
930,
856,
930,
888,
517,
888
],
"score": 0.77,
"latex": "N = 1 , \\pmb { A } = - 1 , \\pmb { B } = 1 , s _ { \\Delta } = \\mathsf { L i n e a r } ( x )"
},
{
"category_id": 13,
"poly": [
417,
692,
436,
692,
436,
712,
417,
712
],
"score": 0.76,
"latex": "\\sigma"
},
{
"category_id": 13,
"poly": [
296,
1034,
321,
1034,
321,
1060,
296,
1060
],
"score": 0.72,
"latex": "\\Delta"
},
{
"category_id": 13,
"poly": [
587,
1507,
614,
1507,
614,
1533,
587,
1533
],
"score": 0.68,
"latex": "\\pmb { A }"
},
{
"category_id": 13,
"poly": [
1374,
1573,
1401,
1573,
1401,
1601,
1374,
1601
],
"score": 0.56,
"latex": "\\pmb { A }"
},
{
"category_id": 13,
"poly": [
893,
857,
930,
857,
930,
889,
893,
889
],
"score": 0.52,
"latex": "( x )"
},
{
"category_id": 13,
"poly": [
516,
858,
585,
858,
585,
887,
516,
887
],
"score": 0.43,
"latex": "N = 1"
},
{
"category_id": 13,
"poly": [
611,
1675,
643,
1675,
643,
1701,
611,
1701
],
"score": 0.38,
"latex": "S 4"
},
{
"category_id": 13,
"poly": [
761,
859,
823,
859,
823,
888,
761,
888
],
"score": 0.28,
"latex": "s \\Delta ="
},
{
"category_id": 15,
"poly": [
707.0,
309.0,
720.0,
309.0,
720.0,
320.0,
707.0,
320.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
931.0,
308.0,
944.0,
308.0,
944.0,
320.0,
931.0,
320.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
1174.0,
316.0,
1215.0,
316.0,
1215.0,
333.0,
1174.0,
333.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
520.0,
335.0,
557.0,
335.0,
557.0,
361.0,
520.0,
361.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
919.0,
335.0,
958.0,
335.0,
958.0,
361.0,
919.0,
361.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
1173.0,
329.0,
1238.0,
329.0,
1238.0,
350.0,
1173.0,
350.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
529.0,
375.0,
549.0,
375.0,
549.0,
391.0,
529.0,
391.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
797.0,
372.0,
823.0,
372.0,
823.0,
395.0,
797.0,
395.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
930.0,
375.0,
949.0,
375.0,
949.0,
391.0,
930.0,
391.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
1022.0,
373.0,
1046.0,
373.0,
1046.0,
393.0,
1022.0,
393.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
1173.0,
372.0,
1236.0,
372.0,
1236.0,
395.0,
1173.0,
395.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
1173.0,
389.0,
1264.0,
389.0,
1264.0,
409.0,
1173.0,
409.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
518.0,
407.0,
559.0,
407.0,
559.0,
432.0,
518.0,
432.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
917.0,
407.0,
960.0,
407.0,
960.0,
432.0,
917.0,
432.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
1171.0,
418.0,
1251.0,
418.0,
1251.0,
444.0,
1171.0,
444.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
1134.0,
438.0,
1150.0,
438.0,
1150.0,
456.0,
1134.0,
456.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
1174.0,
436.0,
1254.0,
436.0,
1254.0,
457.0,
1174.0,
457.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
1174.0,
450.0,
1260.0,
450.0,
1260.0,
470.0,
1174.0,
470.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
519.0,
521.0,
558.0,
521.0,
558.0,
553.0,
519.0,
553.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
628.0,
528.0,
650.0,
528.0,
650.0,
551.0,
628.0,
551.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
705.0,
523.0,
818.0,
523.0,
818.0,
550.0,
705.0,
550.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
947.0,
521.0,
1029.0,
521.0,
1029.0,
552.0,
947.0,
552.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
297.0,
578.0,
1403.0,
578.0,
1403.0,
606.0,
297.0,
606.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
294.0,
602.0,
1405.0,
602.0,
1405.0,
636.0,
294.0,
636.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
295.0,
631.0,
1406.0,
631.0,
1406.0,
662.0,
295.0,
662.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
296.0,
660.0,
1405.0,
660.0,
1405.0,
691.0,
296.0,
691.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
295.0,
686.0,
416.0,
686.0,
416.0,
717.0,
295.0,
717.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
437.0,
686.0,
1358.0,
686.0,
1358.0,
717.0,
437.0,
717.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
293.0,
1893.0,
594.0,
1893.0,
594.0,
1935.0,
293.0,
1935.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
294.0,
1730.0,
710.0,
1730.0,
710.0,
1774.0,
294.0,
1774.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
295.0,
70.0,
849.0,
70.0,
849.0,
109.0,
295.0,
109.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
840.0,
2087.0,
861.0,
2087.0,
861.0,
2118.0,
840.0,
2118.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
295.0,
941.0,
894.0,
941.0,
894.0,
978.0,
295.0,
978.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
972.0,
941.0,
1408.0,
941.0,
1408.0,
978.0,
972.0,
978.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
293.0,
971.0,
577.0,
971.0,
577.0,
1008.0,
293.0,
1008.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
612.0,
971.0,
1405.0,
971.0,
1405.0,
1008.0,
612.0,
1008.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
325.0,
1001.0,
1406.0,
1001.0,
1406.0,
1038.0,
325.0,
1038.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
322.0,
1029.0,
725.0,
1029.0,
725.0,
1068.0,
322.0,
1068.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
1059.0,
1029.0,
1409.0,
1029.0,
1409.0,
1068.0,
1059.0,
1068.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
292.0,
1059.0,
1282.0,
1059.0,
1282.0,
1097.0,
292.0,
1097.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
294.0,
1310.0,
1404.0,
1310.0,
1404.0,
1346.0,
294.0,
1346.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
295.0,
1341.0,
1406.0,
1341.0,
1406.0,
1376.0,
295.0,
1376.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
294.0,
1371.0,
1406.0,
1371.0,
1406.0,
1406.0,
294.0,
1406.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
294.0,
1401.0,
1406.0,
1401.0,
1406.0,
1436.0,
294.0,
1436.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
294.0,
1430.0,
1404.0,
1430.0,
1404.0,
1465.0,
294.0,
1465.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
295.0,
1461.0,
1348.0,
1461.0,
1348.0,
1497.0,
295.0,
1497.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
297.0,
1150.0,
1403.0,
1150.0,
1403.0,
1183.0,
297.0,
1183.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
294.0,
1176.0,
1405.0,
1176.0,
1405.0,
1215.0,
294.0,
1215.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
294.0,
1206.0,
1406.0,
1206.0,
1406.0,
1244.0,
294.0,
1244.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
290.0,
1232.0,
1363.0,
1232.0,
1363.0,
1279.0,
290.0,
1279.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
1397.0,
1232.0,
1410.0,
1232.0,
1410.0,
1279.0,
1397.0,
1279.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
294.0,
1268.0,
891.0,
1268.0,
891.0,
1303.0,
294.0,
1303.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
970.0,
1268.0,
981.0,
1268.0,
981.0,
1303.0,
970.0,
1303.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
295.0,
1506.0,
586.0,
1506.0,
586.0,
1539.0,
295.0,
1539.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
615.0,
1506.0,
1404.0,
1506.0,
1404.0,
1539.0,
615.0,
1539.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
294.0,
1537.0,
599.0,
1537.0,
599.0,
1573.0,
294.0,
1573.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
627.0,
1537.0,
668.0,
1537.0,
668.0,
1573.0,
627.0,
1573.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
834.0,
1537.0,
1262.0,
1537.0,
1262.0,
1573.0,
834.0,
1573.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
1291.0,
1537.0,
1404.0,
1537.0,
1404.0,
1573.0,
1291.0,
1573.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
295.0,
1573.0,
544.0,
1573.0,
544.0,
1606.0,
295.0,
1606.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
625.0,
1573.0,
1373.0,
1573.0,
1373.0,
1606.0,
625.0,
1606.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
293.0,
1599.0,
699.0,
1599.0,
699.0,
1640.0,
293.0,
1640.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
727.0,
1599.0,
1409.0,
1599.0,
1409.0,
1640.0,
727.0,
1640.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
294.0,
1783.0,
1405.0,
1783.0,
1405.0,
1818.0,
294.0,
1818.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
293.0,
1810.0,
1407.0,
1810.0,
1407.0,
1850.0,
293.0,
1850.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
293.0,
1844.0,
787.0,
1844.0,
787.0,
1877.0,
293.0,
1877.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
293.0,
1941.0,
1405.0,
1941.0,
1405.0,
1978.0,
293.0,
1978.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
295.0,
1975.0,
1405.0,
1975.0,
1405.0,
2005.0,
295.0,
2005.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
295.0,
2003.0,
1403.0,
2003.0,
1403.0,
2036.0,
295.0,
2036.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
294.0,
726.0,
1409.0,
726.0,
1409.0,
762.0,
294.0,
762.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
292.0,
753.0,
1406.0,
753.0,
1406.0,
790.0,
292.0,
790.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
294.0,
785.0,
1405.0,
785.0,
1405.0,
821.0,
294.0,
821.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
293.0,
814.0,
392.0,
814.0,
392.0,
852.0,
293.0,
852.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
420.0,
814.0,
1277.0,
814.0,
1277.0,
852.0,
420.0,
852.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
295.0,
1641.0,
1405.0,
1641.0,
1405.0,
1678.0,
295.0,
1678.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
293.0,
1671.0,
610.0,
1671.0,
610.0,
1709.0,
293.0,
1709.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
644.0,
1671.0,
1328.0,
1671.0,
1328.0,
1709.0,
644.0,
1709.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
294.0,
854.0,
515.0,
854.0,
515.0,
894.0,
294.0,
894.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
931.0,
854.0,
987.0,
854.0,
987.0,
894.0,
931.0,
894.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
1049.0,
854.0,
1406.0,
854.0,
1406.0,
894.0,
1049.0,
894.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
293.0,
885.0,
738.0,
885.0,
738.0,
926.0,
293.0,
926.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
953.0,
885.0,
1113.0,
885.0,
1113.0,
926.0,
953.0,
926.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
1399.0,
885.0,
1409.0,
885.0,
1409.0,
926.0,
1399.0,
926.0
],
"score": 1.0,
"text": ""
},
{
"category_id": 15,
"poly": [
297.0,
1104.0,
991.0,
1104.0,
991.0,
1140.0,
297.0,
1140.0
],
"score": 1.0,
"text": ""
}
],
"page_info": {
"page_no": 5,
"width": 1700,
"height": 2200
}
},
{
"layout_dets": [
{
"category_id": 1,
"poly": [
299,
1794,
1405,
1794,
1405,
2035,
299,
2035
],
"score": 0.978
},
{
"category_id": 1,
"poly": [
299,
1574,
1404,
1574,
1404,
1696,
299,
1696
],
"score": 0.975
},
{
"category_id": 1,
"poly": [
299,
1309,
1404,
1309,
1404,
1430,
299,
1430
],
"score": 0.974
},
{
"category_id": 1,
"poly": [
298,
1441,
1405,
1441,
1405,
1563,
298,
1563
],
"score": 0.971
},
{
"category_id": 3,
"poly": [
712,
237,
1393,
237,
1393,
549,
712,
549
],
"score": 0.965
},
{
"category_id": 3,
"poly": [
309,
725,
1390,
725,
1390,
973,
309,
973
],
"score": 0.963
},
{
"category_id": 4,
"poly": [
295,
1000,
1403,
1000,
1403,
1085,
295,
1085
],
"score": 0.953
},
{
"category_id": 1,
"poly": [
297,
1149,
1404,
1149,
1404,
1210,
297,
1210
],
"score": 0.948
},
{
"category_id": 4,
"poly": [
702,
552,
1402,
552,
1402,
636,
702,
636
],
"score": 0.947
},
{
"category_id": 0,
"poly": [
299,
1750,
570,
1750,
570,
1781,
299,
1781
],
"score": 0.907
},
{
"category_id": 0,
"poly": [
300,
1264,
644,
1264,
644,
1295,
300,
1295
],
"score": 0.903
},
{
"category_id": 2,
"poly": [
300,
76,
844,
76,
844,
104,
300,
104
],
"score": 0.895
},
{
"category_id": 2,
"poly": [
841,
2088,
857,
2088,
857,
2111,
841,
2111
],
"score": 0.759
},
{
"category_id": 0,
"poly": [
299,
560,
596,
560,
596,
588,
299,
588
],
"score": 0.142
},
{
"category_id": 1,
"poly": [
296,
559,
666,
559,
666,
643,
296,
643
],
"score": 0.116
},
{
"category_id": 13,
"poly": [
1262,
577,
1345,
577,
1345,
605,
1262,
605
],
"score": 0.91,
"latex": "2 ^ { 6 } = 6 4"
},
{
"category_id": 13,
"poly": [
704,
577,
798,
577,
798,
604,
704,
604
],
"score": 0.89,
"latex": "2 ^ { 8 } = 2 5 6"
},
{
"category_id": 13,
"poly": [
936,
1150,
1016,
1150,
1016,
1179,
936,
1179
],
"score": 0.88,
"latex": "4 0 0 0 \\times"
},
{
"category_id": 13,
"poly": [
929,
1001,
1009,
1001,
1009,
1027,
929,
1027
],
"score": 0.88,
"latex": "{ \\approx } 1 . 3 B"
},
{
"category_id": 13,
"poly": [
812,
1001,
904,
1001,
904,
1027,
812,
1027
],
"score": 0.88,
"latex": "\\approx 1 2 5 M"
},
{
"category_id": 13,
"poly": [
691,
1180,
728,
1180,
728,
1208,
691,
1208
],
"score": 0.86,
"latex": "2 \\times"
},
{
"category_id": 13,
"poly": [
703,
605,
857,
605,
857,
634,
703,
634
],
"score": 0.85,
"latex": "2 ^ { 2 0 } = 1 0 4 8 5 7 6"
},
{
"category_id": 13,
"poly": [
431,
1057,
463,
1057,
463,
1081,
431,
1081
],
"score": 0.46,
"latex": "+ + ^ { \\prime }"
},
{
"category_id": 13,
"poly": [
1356,
1476,
1389,
1476,
1389,
1500,
1356,
1500
],
"score": 0.45,
"latex": "^ { + + }"
},
{
"category_id": 5,
"poly": [
303,
223,
650,
223,
650,
531,
303,
531
],
"score": 0.908,
"html": "